Its quite possible they could find some planet that is similar and they may overcome velocity escape. Modern science is barely 150 years old!
Let me explain:
Let us say that secret research is already anticipating the critical breakaway point of Earth’s sustainability.
They will develop escape vehicles , at tremendous cost, artificial planets, like Galsctoids , which can sustain life indefinitely, that can accommodate a thousand people at one time. galactoids, built at tremendous costs, maybe trillions of dollars each, leaving earth yearly, and secretly funded.
They might set their own course, and relative velocity through time and space will accelerate their time span…
Earthly populations will shrink accordingly, as more poisonous material will decrease quality if life. More people will start to suffer immunological illnesses which will adversely effect therapy, and viruses and bacteria will over come the various therapeutic agents to which they will develop resistance …
The Galsctoids over time can carry millions of healthy people into
voyages of new undiscovered frontiers , planets very similar, in regions yet to be conquered. People that can overcome uncertainty, will at first give immense hope to the general population , by lifting morale, by bringing back a new age of exploration, but as the criticality of earthly existence nears uninhabitable levels, -if voluntary changes of living are not equally as suddenly instituted; the multitudes will panic and struggle to get on board the planetary vessels leaving earth.
The near end will describe a state of meltdown for those who could never leave.
, where Galsctoids can no longer sustain hope of leaving , their production may become impossible, because the plummeting belief that certain groups, can never be qualified to leave., but here is an uncertainty which given enough time, may change.
Those groups will be understood to be as large as 95 percent or more of the population, however a stasis may be reached, with enough people leaving and the rest learning to conserve discourses, that the equation may change to suit indefinite survival mode.
And a turn around, could be arrived at, where subterranean cultures will manage a new sub marginal population, as long as they autonomously could suddenly understand new requirements to change life forms, in order to adept to increased levels of conserving the environmental conditions at that time.
It is inconceivable that such progress can not evolve, and with the overall doubling of knowledge every year or so the odds for such to happen may increase , as the unlikelyhood of it decrease conversely.
Once inter galactic escape is achieved, those aboard the galactic ships will experience a vast change in temporal marking, a year up there could eventually approach total near absolute earthly demarcations of time.
They in fact could return to a time prior to when they left, or return exactly just a few years after leaving, unnoticed, that they actuallt could have spent hundreds or thousands or even millions future earthly years while away.
Calibration of temporal return will be so difficult, however, that when current civilisations presume to notice returnees, they may be perceived as alien spaceships.
Perhaps this stage has already been passed, and our awareness of it may already be known to some researchers.
Jules Verne was quite remarkable for his time, and the view described above is not that much astounding, given the framinf of relative reference.